Uncertainty quantification analysis in the blade element momentum method

Blade element momentum (BEM) theory is a widely used non-linear model for the efficient evaluation of wind turbine performance and design. The aim of this paper is to quantify the uncertainty related to BEM inputs and sub-models, and investigate how these propagate through the model. Uncertainties associated with viscous dissipation in the wake, aerofoil force coefficients, and tip-loss models are considered. The uncertainty quantification (UQ) of these parameters is analysed using non-intrusive polynomial chaos expansion, which provides a structured method for uncertainty propagation and global sensitivity quantification. Sobol’s indices are employed to rank the relative importance of each factor to the overall uncertainty in the system, with a focus on rotor performance and spanwise load distributions. Two BEM implementations with and without tip-loss correction are used to simulate the NREL 5 MW and DTU 10 MW reference wind turbines. Global sensitivity quantification shows that the different rotors may exhibit different levels of sensitivity to input parameters. The effect of viscous mixing in the turbine wake is found to have a significant impact on predicted rotor performance. Uncertainty in tip-loss model coefficients is also found to be generally important, particularly when evaluating spanwise variations in rotor loads. The Sobol’s indices are also observed to depend on the tip speed ratio (TSR), with the most significant uncertainty factors converging for TSR≥6. We additionally compare global sensitivity analysis to local analysis based on partial derivatives of the uncertainty parameters. The non-linear nature of BEM means that a local analysis does not always capture the interactions between different factors, potentially leading to misleading evaluations of parameter importance. UQ has the potential to improve the understanding of BEM, and provide guidance on the importance of sub-model improvements.